↑

Properties

Label 10.5.c
Level $10$
Weight $5$
Character orbit 10.c
Rep. character $\chi_{10}(3,\cdot)$
Character field $\Q(\zeta_{4})$
Dimension $4$
Newform subspaces $2$
Sturm bound $7$
Trace bound $2$

Related objects

Downloads

Learn more

Defining parameters

Level: \( N \) \(=\) \( 10 = 2 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 10.c (of order \(4\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q(i)\)
Newform subspaces: \( 2 \)
Sturm bound: \(7\)
Trace bound: \(2\)
Distinguishing \(T_p\): \(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(10, [\chi])\).

Total New Old
Modular forms 16 4 12
Cusp forms 8 4 4
Eisenstein series 8 0 8

Trace form

\( 4 q + 20 q^{3} - 60 q^{5} - 64 q^{6} + 20 q^{7} + O(q^{10}) \) \( 4 q + 20 q^{3} - 60 q^{5} - 64 q^{6} + 20 q^{7} + 160 q^{10} + 168 q^{11} + 160 q^{12} - 60 q^{13} + 20 q^{15} - 256 q^{16} - 1020 q^{17} - 640 q^{18} + 968 q^{21} + 1280 q^{22} + 1620 q^{23} - 700 q^{25} - 1344 q^{26} + 320 q^{27} - 160 q^{28} + 960 q^{30} - 1112 q^{31} - 1720 q^{33} - 2220 q^{35} + 32 q^{36} - 1020 q^{37} + 960 q^{38} + 1280 q^{40} + 5448 q^{41} - 2240 q^{42} + 660 q^{43} + 6400 q^{45} + 2176 q^{46} + 1620 q^{47} - 1280 q^{48} - 4800 q^{50} - 10712 q^{51} - 480 q^{52} - 4860 q^{53} - 2520 q^{55} + 3072 q^{56} + 5120 q^{57} + 3520 q^{58} - 4960 q^{60} - 7032 q^{61} - 3840 q^{62} + 7700 q^{63} + 7620 q^{65} + 10112 q^{66} + 8660 q^{67} + 8160 q^{68} + 1600 q^{70} + 5928 q^{71} - 5120 q^{72} - 12860 q^{73} - 13100 q^{75} - 5120 q^{76} - 14520 q^{77} - 5760 q^{78} + 3840 q^{80} + 964 q^{81} - 2560 q^{82} - 300 q^{83} + 16580 q^{85} - 14784 q^{86} + 11840 q^{87} - 10240 q^{88} + 9440 q^{90} + 15528 q^{91} + 12960 q^{92} + 2120 q^{93} - 9600 q^{95} + 4096 q^{96} - 13500 q^{97} + 3840 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{5}^{\mathrm{new}}(10, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
10.5.c.a 10.c 5.c $2$ $1.034$ \(\Q(\sqrt{-1}) \) None \(-4\) \(18\) \(-30\) \(58\) $\mathrm{SU}(2)[C_{4}]$ \(q+(-2-2i)q^{2}+(9-9i)q^{3}+8iq^{4}+\cdots\)
10.5.c.b 10.c 5.c $2$ $1.034$ \(\Q(\sqrt{-1}) \) None \(4\) \(2\) \(-30\) \(-38\) $\mathrm{SU}(2)[C_{4}]$ \(q+(2+2i)q^{2}+(1-i)q^{3}+8iq^{4}+(-15+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(10, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(10, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(5, [\chi])\)\(^{\oplus 2}\)